Details

sample161.0ms

Algorithm

intervals

Results

72.0ms	97×	body	1280	valid
40.0ms	24×	body	2560	valid
26.0ms	64×	body	640	valid
8.0ms	28×	body	320	valid
3.0ms	31×	body	80	valid
2.0ms	12×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize9.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (tan (+ x eps)) (tan x))
4.6b	(tan (+ x eps))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `tan-sum` `frac-sub` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

18.0ms	(- (tan (+ x eps)) (tan x))
7.0ms	(tan (+ x eps))

series155.0ms

Counts

2 → 6

Calls

2 calls:

96.0ms	(- (tan (+ x eps)) (tan x))
59.0ms	(tan (+ x eps))

simplify73.0ms

Counts

47 → 47

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	192	420
1	538	319
2	2593	310
3	5001	255
done	5001	255

prune112.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

29.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
9.0ms	(+ (tan x) (tan eps))
16.0ms	(* (tan x) (tan eps))
100.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series808.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
99.0ms	(+ (tan x) (tan eps))
99.0ms	(* (tan x) (tan eps))
383.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify75.0ms

Counts

181 → 181

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	559	2915
1	2054	2366
2	5001	2345
done	5001	2345

prune415.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.1b	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`add-cube-cbrt`
10×	`add-exp-log`
9×	`times-frac`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`tan-quot` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`div-exp` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `frac-times` `rec-exp` `flip3--` `pow-flip` `frac-2neg` `flip3-+` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `distribute-lft-out` `inv-pow` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

11.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
9.0ms	(+ (tan x) (tan eps))
16.0ms	(* (tan x) (tan eps))
0.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

series658.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
101.0ms	(+ (tan x) (tan eps))
101.0ms	(* (tan x) (tan eps))
314.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

simplify42.0ms

Counts

98 → 98

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	367	754
1	1426	679
2	5001	679
done	5001	679

prune297.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 14.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.1b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
40×	`tan-quot`
20×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-r/` `associate-l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-plus` `unswap-sqr`
1×	`pow2` `swap-sqr` `fma-udef`

Counts

4 → 107

Calls

4 calls:

15.0ms	(* (tan x) (tan eps))
16.0ms	(* (tan x) (tan eps))
72.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series963.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (tan x) (tan eps))
100.0ms	(* (tan x) (tan eps))
129.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
635.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify52.0ms

Counts

119 → 119

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	432	1111
1	1952	927
2	5001	872
done	5001	872

prune319.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 14.8b

regimes140.0ms

Accuracy

88.6% (0.8b remaining)

Error of 15.5b against oracle of 14.6b and baseline of 22.0b

bsearch121.0ms

Steps

Iters	Range		Point
10	7.501151066748407e-20	1.7355052557369657e-07	1.1265176979871018e-17
4	-3.4474604111501658e-22	-2.2519064934139983e-22	-3.4100993512209108e-22

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	39
1	36	39
done	36	39

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.4s	3238×	body	1280	valid
1.2s	685×	body	2560	valid
788.0ms	1899×	body	640	valid
225.0ms	755×	body	320	valid
102.0ms	1088×	body	80	valid
69.0ms	335×	body	160	valid